How do you simplify (-15x^4)/( 3x)?

The answer is $- 5 {x}^{3}$.
To simplify $\frac{- 15 {x}^{4}}{3 x}$, we must divide $- 15 {x}^{4}$ by $3 x$. -15 divided by 3 is simple; the answer is -5. I think you might have been strung up on dividing ${x}^{4}$ by $x$. Here is a Quotient property that will help us out: $\frac{{a}^{n}}{{a}^{m}} = {a}^{n - m}$. Using this, we can figure out that ${x}^{4}$ divided by $x$ is ${x}^{3}$ since ${x}^{4 - 1} = {x}^{3}$. In conclusion, the answer is $- 5 {x}^{3}$.